Tilted Squares

We know how to work out the area of a simple square. Use the slider in the activity below to work out the area of a few squares.

We are going to look at the area of tilted squares. By a tilted square I mean something that looks like the squares shown in the image below. We will describe all these squares as having a tilt of 1, since the bottom right corner has been lifted by 1.

What is the area of each of these squares? How can you work it out?What do you notice about the areas of squares with a tilt of 1?Can you predict what the area of the next square with a tilt of 1 will be? Check using the activity below to make the square.

Use the activity to explore the areas of squares with tilt 2, 3 or 4?

Can you make any generalisations about the area of tilted squares?

Ideas for TeachersThis is a great investigation in to the area of tilted squares. A great exploration that is accessible to all abilities, there are many methods pupils could use to work out the areas.You could either use this as is intended, by giving access to this activity to all pupils, or get them to work on squared paper, and use the activity on the board to check their work as they go.Once they have spotted a pattern with squares of a tilt of one, they can look at tilt 2 and so on. The higher abilities will hopefully be able to make some headway in generalising these results, and some might even be able to explain why (a hint towards Pythagoras might push them in the right direction).Either as a quick starter to get the students thinking, or as a whole lesson investigation, this activity can be used in any classroom.

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